Long-term cross-border electricity trading model under the background of Global Energy Interconnection

1 Introduction

The rapid development of ind ustrialization and urbanization in the last few centuries has led to severe environmental pollution and climate change problems worldwide.The key pollutants that have caused global environmental issues largely come from the burning of fossil fuels to meet energy demand.The major pollutants problems sulfur dioxide,leading to acid rain,nitrogen oxide,producing smog,and carbon dioxide,driving the global warming.Therefore,it is critical that more efforts need to be made on the development of new and clean sources of energy rather than the continued reliance on fossil fuels[1-3].

Clean and renewable energies such as solar power,wind power,and hydro power represent excellent alternatives to fossil fuels.These clean and renewable energy sources have unexhausted reserves worldwide and are environmentally friendly; their strategic development could potentially satisfy the increasing energy demands of human societies.Nevertheless,the allocation and distribution of clean and renewable energy resources is largely unbalanced among countries and regions.Usually,load centers are in the plain areas,which are crowded but lack clean and renewable energy,and renewable energy bases are located far away from the load centers,such as in the Arctic and Sahara regions.

Nowadays,the concept of global energy interconnection(GEI) is gaining more attention,and the aim is to develop a global power grid that can transmit the electrical power converted from renewable energy resources and other forms of energy worldwide [4,5].Based on the background issues discussed above and the GEI concept,it is clearly important to study the possibility of cross-border electricity trading,which could be the key to solving the problem of geographical mismatches between clean energy production and consumption,and to the promotion of the optimal allocation of clean energy resources across a worldwide scale [6].

Several scholars have conducted research on the trading mechanisms,but these studies have mainly focused on cross-provincial power transactions [7-13].Reference[10] proposed an operation mechanism that included contract standards,trading modes,and bidding rules,and it was found to be suitable for the Chinese power market.Reference [14] investigated the relationship between energy production and cross-border power transmission in Europe by statistical analysis.As the first cross-border market in the world,the Nordic market can boast of its successful organizational and operational experiences,which are worthy of intense study [13].However,these tools may not be applicable in other regions or countries where the scale spans over diverse geographical areas and targets.

Regarding the large-scale clean and renewable energy integration,wind power brings about great uncertainty to multinational power system supply estimations and cross-border electricity trading.Moreover,it increases the difficulty of cross-border electricity trading contract decomposition and scheduling for power generation plans.Contract decomposition and generation schedules have become urgent problems to be solved in cross-border electricity trading design work around the world.In contract decomposition,the key issues are the principle and time scale of decomposition.For the generation schedule,the uncertainty of wind power should be considered in a windhydro-thermal coupled power system.Thus,this paper presents a long-term transnational model for energy with the objective of achieving maximum social welfare.In the proposed method,a scenario analysis method is used to deal with the uncertainty of wind power,and a stochastic optimization method is proposed to solve the uncertainty model.In the model,the cross-border transmission tariff and the potential benefit risk are also taken into the consideration.

The structure of this paper is as follows.The crossborder annual matching transaction model considering cross-border interconnection development benefits and potential benefit risk costs is built in Section II.In Section III,the annual contract decomposition model and the generation schedule model are built.Section IV gives an example based on practical experiences in the area of northeast Asia,and Section V summarizes the present paper.

2 Cross-border annual transaction model

2.1 Electricity transmission cost

A reasonable electricity transmission cost mechanism will promote and guide optimal cross-border electricity transaction.Calculating more accurately and apportioning more fairly are key issues of the transmission cost mechanism.

The electricity transmission cost CTR mainly consists of the following parts:

where Cbase,k,Coperate,k,and Ctrloss,k represent the construction cost,operation cost,and losses of transmission line k,respectively.εk,ci n itial, k ,and δk represent the discount rate,initial investment cost,and operation and maintenance rate of transmission line k, respectively.Pt,k,βtr,k,and Vtr,Y,k represent the transmission price,line loss rate,and yearly transmission volume of transmission line k, respectively.

The improved MW-Miles method was used to apportion the electricity transmission costs among the dealers:

where γk represents the average cost of transmission line k per MW-Miles.Cc,k and Coperate,k represent the transmission capacity cost and the operation cost of transmission line k,respectively.Pcrit,k and Lk represent the delivery power and length of transmission line k,respectively.

2.2 Cross-border power trade influence factors

Here,we build an influence index system by considering the cross-border interconnection development benefits and potential benefit risks.

2.2.1 Cross-border interconnection development benefits

The Global Energy Interconnection Development and Cooperation Organization (GEIDCO) has built the global energy interconnection development index (GEIDI) based on GEI and a comprehensive evaluation method.GEIDI can reflect the development level of countries from the following three dimensions:power interconnection among countries,low carbon features,and the coordinated development of the energy economy and social environment [15].

The cross-border interconnection development benefit of transmission line k can be calculated as follows:

where αG is the coefficient of GEIDI,which represents the benefit of the transmission per megawatt-hour (MWh)at a certain GEIDI level.Vtr,Y,k is the annual transmission electricity of transmission line k,and the interconnection development trading benefit of electricity transaction l is written as follows:

2.2.2 Cross-border potential benefit risk

Risks of trading loss should be valued during the crossborder electricity trading.Nowadays,many institutions such as The EIA (Economist Information Agency) and the PRS (Political Risk Service) Group have engaged in much work to assess the risks of national trading.Among them,The PRS Group carries out risk assessments based on 12 indicators,which include data on the extent of social economic environment,domestic conflicts,and external conflicts,and the approach produces a comprehensive potential benefit risk index Ri (full score is 100) for country i.For this,set the potential benefit risk index Rij between country i and j as the mean value of Ri and Rj.The lower the Rij is,the higher the potential benefit risk.

All power transmission lines should be traversed before matching transactions,and the transaction cannot be reached if the risk index is below the threshold value.For transactions that can be matched,calculate the loss of potential benefit in the form of risk cost.The risk cost of the electricity transmission line k is as follows:

where α is the potential benefit risk coefficient,which means the risk cost per megawatt-hour (MWh) at a certain risk level.

The risk cost of electricity transaction l is as follows:

2.3 Cross-border annual matching transaction model

Most regional cross-border electricity markets worldwide are still in their infancies,and we used a concentrated trading mode to match the annual transactions.

The matching transaction model uses the maximum social benefits as the objective function.Then,the objective function of the improved matching transaction is obtained:where m,n are the number of electricity buyers and sellers.Vi,j represents the amount of electricity purchased from seller j by buyer i.and andrepresent the centralized and decentralized transaction electricity,respectively.Bi ( V i , j ),S j ( V i , j ) represent the purchase cost of buyer i and sale income of seller j,respectively.VBi,max and VSj,max represent the maximum declared-electricity of a buyer and seller,respectively.VT,k represents the maximum electricity transmission volume of transmission line k.CTR,k represents the transmission cost of transmission line k.

3 Annual contract decomposition and the generation schedule

Trading contracts should be divided into monthly or weekly contracts for delivery after the annual transactions have been determined.However,the uncertainty and prediction inaccuracies for renewable energy like wind power increases the difficulty of trading contract decomposition and generation scheduling.

Therefore,in this section,a long-term wind-hydrothermal generation schedule model considering the uncertainty of wind power is established.

3.1 Annual contract decomposition

In the hybrid wind-hydro-thermal power system,by considering both the uncertainty of wind power and the regulation of hydropower,the proposed model decomposes the annual trading contract into monthly contracts.

The cultural differences between countries can also influence the monthly electricity allocation.We employ load curves and the marginal cost of generation as tools to reflect the different national conditions (e.g.,differences in holidays and electricity supply-demand relationships).Besides,due to the involvement of cross-border trading,a unified settlement currency is required.Thus,the variation of the exchange rate also has an impact on electricity trading,especially for settlements.

Generation costs are mainly related to thermal power generation because wind power and hydropower have no generation costs.Decomposing the contract according to the coal price can minimize the generation costs,yet this may cause an imbalance of the power supply.Therefore,we added a power deficiency penalty function to optimize the electricity decomposition.

where λi, t represents the coal cost of seller i at month t.Vi,j,t represents the monthly transaction electricity at montht.EENS represents the expected value of the electricity deficiency.

where pi,t represents the electricity deficiency probability of seller i at month t.ΔL i, t represents the electricity deficiency at month t caused by seller i.VOLL represents the coefficient of the electricity deficiency penalty.

3.2 Scenario analysis

First,an annual trading contract is decomposed into four periods,and the quarterly wind power output is divided into three states,which represent high,middle,and low levels.Based on this,define the yearly multi-stage wind power output scenarios as the wind power output value at quarterly intervals over the yearly scale.Then,the scenarios are selected by fast forward scenario selection (FFSS)algorithm.

The FFSS algorithm is designed to eliminate the scenarios of high similarity,so that the reserved scenario set can reflect the features of the original scenario set with a small number of scenarios.The selection process is as follows:

(1) Calculate the distance dku=d(ωk,ωu) between scenarios and the probability distance Du between each scenario and others.

(2) Find theω0 for which D0=min Du

(3) Eliminate ω0and redistribute the probability to ensure the sum of the remaining scenarios' probability is 1.

(4) Judge the terminating condition; stop iteration if the remaining scenarios satisfy the requirement.Otherwise,go back to step one and repeat the above steps.

3.3 Wind-hydro-thermal power unit commitment objective function

The running cost of pumped storage power stations is generally neglected.Therefore,the main cost is the start-up cost for pumped storage units,so the hydropower optimal function is as follows:

where CHydro represents the generation cost of the pumped storage unit. represents the start-up cost of the pumped storage unit as it changes from the discharge state to pumped state. represents the shutdown cost of the hydropower unit.ip,t and ig,t are binary variables.ip,t indicates the pumped state of the unit,and 1 stands for pumped and 0 for discharge.When the unit is in a discharge state,

The generation cost of the thermal power mainly consists of the running cost and start-up and shutdown costs:

The generation schedules of the hydropower and thermal power stations would contain randomness for the uncertainty of the wind power energy.Thus,the objective function of the hydro-thermal unit commitment can be expressed as follows:

Set ps as the probability of scenario S,and ps ＞0, so the stochastic programming model of thermal unit commitment can be built:

where T represents the total number of programming stages,which equals 12 in this study. represents the output of thermal unit h under scenario s during period t.and represents the start-up cost and shutdown cost of thermal unit h under scenario s during period t, respectively. represents the production cost of unit h under scenario s during period t,which can be calculated as follows:

where ah,bh,and ch represent coefficients of the quadratic production cost function of thermal unit j.

3.4 Wind-hydro-thermal power unit commitment constraints

The constraints are as follows:

1.Trading contract constraint

where Tw represents the scheduling cycle,and Tw=720 h.Ew,s,t represents the monthly transaction electricity under scenario s. represents the wind power output under scenario s during period t.

2.Hydropower generation constraints

(1) Available power output constraints

(2) Unit logic constraints

(3) Water consumption constraints

The conversion function of water consumption and output of the hydropower unit is as follows:

where PHydro represents the output of the hydropower unit.aH,bH,cH,dH represent the coefficients of the production cost function of the hydropower unit.

3.Thermal power generation constraints

(1) Reserve constraints; adjust reserve constraint

where rr represents the coefficient of the adjust constraint.Lt represents the load demand at period t.

(2) Spinning reserve constraint

where rs represents the coefficient of spinning reserve.(3) Available power output constraints

where and represent the minimum and maximum output of thermal unit h.Ih,d,s is a binary variable that indicates the on/off state of generator h under scenario w at day d; 1 stands for on and 0 for off.

(4) Ramping constraints

(5) On/off time constraints

Set one day as the time interval of the thermal units that participate in the monthly commitment,and the minimum on/off time can be several days.Thus,the constraints of the generators are as follows:

where and represent the minimum start time and minimum shutdown time of thermal unit h.

(6) Start-up and shutdown time constraints

The start-up and shutdown times of a generator are within the maximum times.

4 Case study

We chose the Russia Far East area (RUS),Mongolia(MGL),north China and northeast China area (CHN),South Korea (KOR),North Korea (PRK),and Japan (JPN) as examples to perform the case study.Fig.1 shows the sketch map of the northeast Asian power system

The Russia Far East is rich in hydropower resources,and this area as well as north and northeast China and southeast Mongolia are rich in wind power resources.Therefore,we set four pumped storage power stations and three wind power stations in RUS,four wind power stations in CHN,and three wind power stations in MGL.The transaction data is shown in Table1.

Fig.1 Sketch map of the northeast Asian power system

Table1 Power transaction data (105 MWh)

(negative value means buy in)

Country RUSMGLCHN PRK KOR JPN Declared electricity(105 MWh) 1300 600 1800 -800 -1200 -1050 Declared price(106$) 4.15 3.67 4.64 -6.53 -7.05 -7.39

Referring to the potential benefit risk index released by PRS [16],the trading potential benefit risk index Rtr between country i and j is the mean value of Ri and Rj,and potential benefit risk data is shown in Table2.

Table2 Potential benefit risk of the transmission line

line number 1 2 3 4 5 6 7 Rtr 61.25 61 66 63 62 64.25 60.5

The capacity of the power transmission line is as follows:

Table3 Capacity of the power transmission line [17]

No.Interconnected country/region Capacity (MW)1 MGL CHN 10,000 2 CHN RUS 36,000 3 CHN PRK 11,500 4 PRK KOR 13,000 5 CHN KOR 22,400 6 KOR JPN 28,000 7 RUS JPN 110,000

Matching the transaction according to the data declared by the bidders.Set the decentralized trading between Russia and China,North Korea and South Korea,and South Korea and Japan,and set Rk0=60,α= 0 .03; the matching transaction results are as follows:

Table4 Annual transaction results (Rk0= 60,105 MWh)

(B:buyer; S:seller)

B RUS MGL CHN PRK KOR JPN S RUS MGL CHN VD=500 PRK VC=800 KOR VC=600 VC=VD=400 600300 JPN VC=1050 VD=

Set Rk0=61 (the power transmission through line 7 cannot be reached),and the matching results are as follows:

Table5 Annual transaction results (Rk0= 61,105 MWh)

B RUS MGL CHN PRK KOR JPN S RUS MGL CHN VD=600 PRK VC=650 VC=150 KOR VC=600 VC=VD=600400 S VC=VD=1050400

The social welfare decreased from 8.8625×108 $ to 7.9768×108 $ when transmission line 7 was interrupted.We can see that through cross-border trading,the social benefit can be increased,yet we should remain on guard as to the potential benefit risk and take measures to deal with it.

Next,we use data in Table4 to decompose the annual transaction contract into weekly contracts.The decomposition is mainly according to characteristics of the bidder's load and the allocation results are presented in Fig.2.

Fig.2 Weekly transaction composition

Fig.3 The 12-stage output scenario for wind power

Here,transactions between Mongolia and Korea are chosen for an example.Three output values were reserved of each stage,which represent high,middle,and low level respectively.Fig.3 shows the multi-stage output of wind power,and the solid line shows one of the multi-stage wind power output scenarios.(The permeation ratio of wind power is 20%).

Next,we use the results of RUS as an example to show the thermal generation plan for a month.Thermal generator No.86 and No.87 are set as regulating units.Fig.4 shows the thermal generation plan under different conditions.

The penetration of wind power can increase the volatility of wind-thermal system and thermal units have to start-up and shut-down to smooth the volatility.From Fig.4(a) and Fig.4 (b) we can see that the fluctuation of thermal unit commitment increased,especially the No.86 and No.87.Frequent start-up and shutdown of thermal units can increase operating costs,and the regulating ability of windthermal system is limited.

Complementary exists between hydropower and wind power,and hydropower units can play the role of peak shaving.It can be seen from Fig.4 (c) that hydropower units can relieve the fluctuation of thermal commitment caused by wind power.It also reduce utilization hours of thermal power units,which leads to the reduction in the system total operation cost by optimizing the allocation of cross-regional clean energy resources.

Fig.4 Portion of the stochastic thermal unit commitment results

5 Conclusions

The long-term cross-border trading model proposed in this study combines centralized transactions with decentralized transactions,which can maintain the market's stability as well as the market's vigor.Numerical results from the case study show that the optimal allocation of resources can be realized through cross-border electricity trading.The consideration of the interconnection development benefits and potential benefit risks among countries conform to the characteristics of the cross-border transactions.Yet,it is necessary to strengthen the market risk assessment and take effective measures to minimize loss caused by potential benefit risk factors; the combination of the scenario analysis method with the stochastic programming can efficiently solve the uncertainty problem brought about by wind power and thus realize the crossborder configuration of power resources.Importantly,the model proposed in this study can be used as theoretical guidance during the design of cross-border power trading mechanisms.